Conventionally, there is known a bifuel vehicle which switches between the use of gas fuel such as CNG (Compressed Natural Gas) and the use of liquid fuel in order to realize the low emission. For example, in Patent Reference-1, there is disclosed a technique which switches the fuel from gasoline to the gas fuel in addition to the fuel cut so that the supply of gasoline to the engine is stopped in response to the satisfaction of a predetermined switching condition for switching the fuel from gasoline to the gas fuel and that the gas fuel is supplied to the engine after a predetermined duration has passed. In Patent Reference-2, there is disclosed a technique which is related to the present invention.    Patent Reference-1: Japanese Patent Application Laid-open under No. 2006-161804    Patent Reference-2: Japanese Patent Application Laid-open under No. S62-096742